96-221 C. Landim, S. Olla and H.-T. Yau

First order correction for the hydrodynamic limit of asymmetric simple exclusion processes in dimension $d\ge 3$. (388K, ps) May 22, 96

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Abstract. It is well known that the hydrodynamic limit of the asymmetric simple exclusion is governed by a viscousless Burgers equation in the Euler scale [R]. We prove that, in the same scale, the next order correction is given by a viscous Burgers equation up to a fixed time $T$ for dimension $d \ge 3$, provided that the corresponding viscousless Burger equation has a smooth solution up to time $T$. The diffusion coefficient was characterized via a variation of Green-Kubo formula by [V, X, EMY]. Within the framework of asymmetric simple exclusion, this provides a rigorous verification for the interpretation of analogous phenomena that the correction to the Euler equation is given by the Navier--Stokes equation if the time scale is within the Euler scale.

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